A Perturbative Treatment of The CoOrbital Motion
Abstract
We develop a formalism of the nonsingular evaluation of the disturbing function and its derivatives with respect to the canonical variables. We apply this formalism to the case of the perturbed motion of a massless body orbiting the central body (Sun) with a period equal to that of the perturbing (planetary) body. This situation is known as the ‘coorbital’ motion, or equivalently, as the 1/1 mean motion commensurability. Jupiter's Trojan asteroids, Earth's coorbital asteroids (e.g., (3753) Cruithne, (3362) Khufu), Mars' coorbital asteroids (e.g., (5261) Eureka), and some Jupiterfamily comets are examples of the coorbital bodies in our solar system. Other examples are known in the satellite systems of the giant planets. Unlike the classical expansions of the disturbing function, our formalism is valid for any values of eccentricities and inclinations of the perturbed and perturbing body. The perturbation theory is used to compute the main features of the coorbital dynamics in three approximations of the general threebody model: the planarcircular, planarelliptic, and spatialcircular models. We develop a new perturbation scheme, which allows us to treat cases where the classical perturbation treatment fails. We show how the families of the tadpole, horseshoe, retrograde satellite and compound orbits vary with the eccentricity and inclination of the small body, and compute them also for the eccentricity of the perturbing body corresponding to a largely eccentric exoplanet's orbit.
 Publication:

Celestial Mechanics and Dynamical Astronomy
 Pub Date:
 April 2002
 DOI:
 10.1023/A:1015219113959
 Bibcode:
 2002CeMDA..82..323N
 Keywords:

 restricted threebody problem;
 disturbing function;
 mean motion resonances;
 Lagrange equilibrium points;
 coorbital motion;
 Trojan asteroids